gaw gaw der-splunk

"oh, that's an invalid argument" replied the bitler, "the horsegas isn't cringeworthy"
"what" said Lrs. Wodgeworthy "do you mean?" lhe asked most precipitouslessly.
"you agree" said the bitler "that if one thing is held to be the same as another thing, then the two things are in fact, one, no?"
"i know, i know! it's a watermelon!" replied Lrs. Wodgeworthy.
"um. anyway. if two things are in fact one thing, then we have ensconced division!"
"isn't that illegal in Wilbertville" retorted Lrs. Wodgeworthy.
"i am attempting to argue (under some duress), that if we hold one thing to be the same as another thing, then if we can perfectly confuse that thing for something else, we have removed all distinctions between them: we can no longer discriminate between them. this is the essence of division."
"so the essence of division is illegal in Wilbertville" replied Lrs. Wodgeworthy.
"as a foil, you're completely useless, you know." blarbled the bitler.
"first outer inner last" algebraicised Wodgeworthy.
"so I was saying, if the essence of division is the explicit and intentional blurring of the differences and distinction between two things such that they are regarded as the same and consequently we are left with one thing and a thing divided: a piece of information which is distilled out from the process of division. in most cases these are both numbers but only one of them might be a number and the other might not. in purely abstract operations on numbers, two numbers are distilled out: this is factorization." blarbled the bitler.
"you're an excellent tho' longwinded didactic device." skeedged Lrs. Wodgeworthy.
"at least you're getting metaconversational. I bet you twelve root seven ducats that you're the first one to break the fourth wall." expingulated the bitler.
"you're on. so you were saying..." responded Wodgeworthy.
"nits picked and cantilevers precisely balanced with the restoration of information and multiplication, and swerving purple at the horizon, is it no surprise that when mathematicians consider the edgy balance that addition and multiplication reach with the primes, they're led on a magical mystery tour that brings them straight to the cosmic galois group." coughed the bitler.
"I protest" (Wodgeworthy is being used as an advocate of common sense here) "the analogy that you're trying to draw between a so-called fundamental object / cosmic or cosmological galois group regardless of scope or reasoning system is rather uncalled for. "

"But what" replied the Bitler "would the mathematician's Philosopher's Stone be?" -- "a cosmic and transcendental dictionary that would be able to interpolate between any theorem or mathematical structure and any other? Sure, the best they can do at the moment is yammer on about their particular specialties, but just imagine what you could do with such a thing. Rather than trying harried operations to express two different mathematical objects in two different categories or toposes using appropriate functors to image one to another, one would have this massively powerful structure representor/transformer. It wouldn't be the transformation group of the symmetries of the line or the plane, or a twenty four dimensional orbifold, or the Riemannian manifold of which E8 is the group of symmetries for. Take two mathematically disparate objects, like the monster group M and the julia set for sin(z) for z a quaternion. Now, you could force many relationships between them, but they'd all be hackneyed and unnatural. If you had the cosmic group, and I don't mean the cosmic galois group of the rationals that everyone's all ga-ga about at the moment, but The Cosmic Thang which connects J. Random X mathematical thingie to J. Random Y mathematical thingy in the most natural and supremely transparent manner, you could transform/connect/interpolate one thing to another. But it is not this quality which gives The Cosmic Thang it's nifty features. One can imagine finding unexpected rivulets and other stranger treasures presently undreamt of..." babbled the bitler.
"the reader is definitely bored now" yammered Wodgeworthy.
"you broke the fouth wall. those ducats are mine" yarrowed the bitler.